There are two rectangular plots of land L1 and L2 The differ

There are two rectangular plots of land, L1 and L2. The difference between the length and width of L1 is 3 m. The length of L1 is 8 m more than....

that of L2; the width of L1 is 5 m less than that of L2 and the area of L2 is 250 m^2 more than half that of L1. Find the lengths and widths of L1 and L2.

Solution

Let the Length of L1 be X m

Let the Width of L1 be X + 3 m

Let the Length of L2 be X - 5 m

Let the Width of L2 be X + 5 m

Area of L1 = x ( x + 3 ) = x^2 + 3x

Area of L2 = ( x - 5 ) ( x + 5 ) = x^2 - 25

x^2 - 25 - ( x^2 + 3x ) / 2 = 250

2 ( x^2 - 25 ) - ( x^2 + 3x ) = 500

2x^2 - 50 - x^2 - 3x = 500

x^2 - 3x - 550 = 0

( x - 25 ) ( x + 22 ) = 0

x = 25 or x = - 22 ( rejected )

Length of L1 = 25 m

Width of L1   = 28 m

Length of L2 = 20 m

Width of L2   = 30 m